Whoever said that royals earn their royal titles? A hereditary monarchy doesn't work that way.
Of course you are right, but still I think the times have change and the "world" (public and media) is not longer willing to let "princesses" get away with everything only because they are born a princess. Stephanie of Monaco learned some lessons about this, I guess and a lot of other princesses are to cautious to play the peacock for a willing/unwilling crowd.
I don't believe people want people's princesses. Because people already have their "people's people" - their politicians they can select through votes. So once the princesses that are forced on the people become little barbies in the sense that these princesses live the dreams of any young barbie girl, then that's annoying and leads to feelings of envy and the question if their pampered life makes any sense.
And: do people nowadays really want hereditary monarchies with all the people attached to it by blood? I don't think so. There are certain expectations even in the smallest village of how the respective "lady of the manor" should behave and if she doesn't she'll fast find herself cast in a different and not so pleasant role. Same with "Royals" who don't behave or who don't have value for the community.
When we talk about society and society's expectation here, we should realise that people supporting the monarchy do that because of the tradition this institution represents and because of the actual people being the representatives. Beatrice through her behaviour does not at the moment embody the institution of the past and she is IMHO not yet the personality to make people believe in the value and sense of this institution.
That is quite normal for a young lady, for any young lady, agreed but what she does is thwart the institution .
The monarchy has not been the perfect way to organise a nation, but it's concentration on a leading personage with a (more or less) clear claim to rule has lead to a certain stability. Nowadays it's enough to have this person on top and a suitable heir. And there are alternative ways to organize a nation. So all other family members can potentially become a problem if they don't fit in.
Even Diana as a young bride (and a teenager) understood the reasoning behind the way she was, wel,. let's say, encouraged to lead her life as member of the RF. And she did it in great style without falling for the temptation to live Barbie's dreams. Even later she was able to mix her fun with a genuine enough care for other members of the society she lived in.
And I don't see that in Beatrice at the moment.